Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination: $8x+5y=9$, $3x+2y=4$

• A. $x=1$ and $y=7$
• B. $x=-3$ and $y=4$
• C. $x=-2$ and $y=5$
• D. $x=0$ and $y=1$

Answer 1

The correct option is C $x=-2$ and $y=5$

Multiply the equation $8x+5y=9$ by $3$ and equation $3x+2y=4$ by $8$ to make the coefficients of $x$ equal. Then we get the equations:

$24x+15y=\mathrm{27.........}\left(1\right)$

$24x+16y=\mathrm{32.........}\left(2\right)$

Subtract Equation (1) from Equation (2) to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(24x-24x)+(16y-15y)=32-27$

i.e. $y=5$

Substituting this value of $y$ in the equation $8x+5y=9$, we get

$8x+25=9$

i.e. $8x=-16$

i.e. $x=-2$

Hence, the solution of the equations is $x=-2,y=5$.